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High order PDE-convergence of AMF-W methods for 2D-linear parabolic problems

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Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu,

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Abstract.The orders of PDE-convergence in the Euclidean norm of s-stage AMF-W-methods for two dimensional parabolic problems on rectangular domains are considered for the case of Dirichlet boundary conditions and an initial condition. The classical algebraic conditions for order p with p≤ 3 are shown to be sufficient for PDE-convergence of order p (independently of the spatial resolution) in the case of time independent Dirichlet boundary conditions. Under additional conditions, PDE-convergence of order p=3.25-ε for every ε >0 can be obtained. In the case of time dependent boundary conditions the order reduction is more dramatic, but order p=2.25- ε for every ε >0 can be achieved.

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Key Words. Parabolic problem, AMF-W method, PDE-convergence, order conditions, fractional order.

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